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Time
Time has been studied by philosophers and scientists for 2,500 years, and thanks to this attention it is much better understood today. Nevertheless, many issues remain to be resolved. Here is a short list of the most important ones—what time actually is; whether time exists when nothing is changing; what kinds of time travel are possible; why the time dimension has an arrow but a space dimension does not; whether the future and past are real; how to analyze the metaphor of time's flow; whether the future will be infinite; whether there was time before the Big Bang; whether tensed or tenseless concepts are semantically basic; what is the proper formalism or logic that captures the special role that time plays in reasoning; and what are the neural mechanisms that account for our experience of time. Some of these issues will be resolved by scientific advances alone, but others require philosophical analysis.
Philosophers of time are deeply divided on the question on what sort of ontological differences there are among the present, past and future. Presentists argue that necessarily only present objects and present experiences are real; and we conscious beings recognize this in the special "vividness" of our present experience. The growing-universe theory is that the past and present are both real, but the future is not yet real. The more popular alternative theory is that there are no significant ontological differences among present, past and future. This view is called "eternalism" or "the block universe theory."
This raises the issue of tenseless versus tensed theories of time. Eternalism or the block universe theory implies a tenseless theory. The earliest version of this theory implied that tensed terminology (such as "will win" within the sentence "The Lakers will win the basketball game") is not semantically basic, but instead is analyzable into tenseless terms (such as "does win at time t" and "happens before" and "is simultaneous with"). Once all tenseless facts are fixed, all tensed facts are thereby fixed. Later versions of the tenseless theory do not imply that tensed terminology is removable or reducible, but only that the truth conditions of tensed remarks can be handled with tenseless facts. On the other hand, advocates of a tensed theory of time say that tenseless terminology is not semantically basic but should be analyzed in tensed terms, and that tensed facts are needed to make the tensed statements be true. For example, a tensed theory might imply that the world involves irreducible tensed properties such as presentness or now-ness or being-in-the-present, and no adequate account of the present tensed fact that it's now midnight can be given without these tensed properties. So, the philosophical debate is over whether tensed concepts have semantical priority over untensed concepts, and whether tensed facts have ontological priority over untensed facts.
This article explores both what is now known about time and what is controversial and unresolved, by addressing the following questions:
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Table of Contents (Clicking on the links below will take you to those parts of this article)
1. What should a philosophical theory of time do?
2. How is time related to mind?
3. What is time?
4. What does science require of time?
a. Relatvity and Quantum Mechanics
b. The Big Bang
c. Is time infinite?
d. Atoms of time
5. What kinds of time travel are possible?
6. Is the relational theory of time preferable to the absolute theory?
7. Does time flow?
8. What gives time its direction or "arrow"?
a. What needs to be explained?
b. Explanations or theories of the arrow
c. Multiple arrows
d. Reversing time
9. Is only the present real?
10. Are there essentially tensed facts?
11. What is temporal logic, the symbolic logic of time?
12. Supplement of frequently asked questions:
What are proper times, coordinate systems, and Lorentz transformations?
What are instants and durations?
What is an event?
What is a reference frame?
What is an inertial frame?
What is spacetime?
What is a Minkowski diagram?
What are the metric and the interval?
Does the theory of relativity imply time is partly space?
Is time the fourth dimension?
Is there more than one kind of physical time?
How is time relative to the observer?
What are the relativity and conventionality of simultaneity?
What is the difference between the past and the absolute past?
What is time dilation?
How does gravity affect time?
What happens to time near a black hole?
What is the solution to the twins paradox (clock paradox)?
What is the solution to Zeno's paradoxes?
How do time coordinates get assigned to points of spacetime?
How do dates get assigned to actual events?
What is essential to being a clock?
What is our standard clock?
Why are some standard clocks better than others?
13. References and Further Reading
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1. What should a philosophical theory of time do?
Should it define "time"? Yes, but it is improper to demand that we define our term "time" as a prelude to saying anything more about time, in large part because as we've learned more about time our definition of time has evolved. What we really want is to build a comprehensive, philosophical theory of time that helps us understand time, say, by helping us solve problems about time. We don't want to start building this theory by adopting a definition of time that prejudices the project from the beginning.
Although there are theories of how to solve a specific problem about time, it is always better to knit together solutions to several problems. Ideally, the goal is to produce a theory of time that will solve in a systematic way the constellation of problems involving time. What are those problems?
One is to clarify the relationship between time and the mind. Does time exist for beings that have no minds? It is easy to confuse time itself with the perception of time.
Another problem is to decide which of our intuitions about time should be retained. Some of these intuitions may reflect deep insights into the nature of time, and others may be faulty ideas inherited from our predecessors. It is not obvious which is which. For one example, if we have the intuition that time flows, but our science implies otherwise, then which view should get priority? Philosophers of time must solve the problem of how to treat our intuitions.
A third problem for a philosophical theory of time is to clarify what physical science presupposes and implies about time. A later section of this article examines this topic. Most all philosophers of time claim that philosophical theories should be consistent with physical science, or, if not, then they must accept the heavy burden of proof to justify the inconsistency.
A philosophical theory of time should describe the relationship between instants and events. Does the instant that we label as "11:01 A.M." for a certain date exist independently of the events that occur then? In other words, can time exist if no event is happening? This question or problem raises the thorny metaphysical issue of absolute vs. relational theories of time.
A theory of time should address the question of time's apparent direction. If the projectionist in the movie theater (cinema) shows a film of cream being added into black coffee but runs the film backwards, we in the audience can immediately tell that events couldn't have occurred this way. We recognize the arrow of time because we know about the one-directional processes in nature. This arrow becomes less and less apparent to us viewers as the film subject gets smaller and smaller and the time interval gets shorter and shorter until finally we are viewing processes that could just as easily go the other way, at which point the arrow of time has disappeared. Philosophers disagree about the explanation of the arrow. Could it be a consequence of the laws of science? The arrow appears to be very basic for understanding nature, yet it is odd that asymmetries in time don't appear in the principal, basic dynamical laws of physics. Could the arrow of time reverse some day? Philosophers wonder what life would be like in some far off corner of the universe if the arrow of time were reversed there. Would people there walk backwards up steps while remembering the future?
Another philosophical problem about time concerns the two questions, "What is the present, and why does it move into the past?" If we know what the present is, then we ought to be able to answer the question, "How long does the present last?" Regarding the "movement" of the present into the past, many philosophers are suspicious of this notion of the flow of time, the march of time. They doubt whether it is a property of time as opposed to being some feature of human perception. Assuming time does flow, is the flow regular? With some theories time, we can make sense of Friday seconds lasting much longer than Thursday seconds, as the flow of Friday time slows to a crawl.
Some philosophers doubt whether the future and past are as real as the present, the feature that is referred to by the word "now." A famous philosophical argument says that, if the future were real, then it would be fixed now, and we would not have the freedom to affect that future. Since we do have that freedom, the future can't be real. Some philosophers consider this to be a clever, but faulty argument.
For a last example of a philosophical issue regarding time, is time a fundamental feature of nature, or does it emerge from more basic features--in analogy to the way the smoothness of water flow emerges from the complicated behavior of the underlying atoms? From what more basic feature does time emerge?
A full theory of time should address this constellation of philosophical issues about time. Narrower theories of time will focus on resolving a few members of this constellation, but the long-range goal is to knit together these theories into a full, systematic, detailed theory of time.
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2. How is time related to mind?
Physical time is public time, the time that clocks are designed to measure. Psychological time is private time. It is best understood as being consciousness of physical time. Psychological time passes slowly for someone who is waiting anxiously for the water to boil on the stove, and it passes swiftly for someone enjoying a book and paying no attention to the water on the stove. Some philosophers claim that psychological time is completely transcended in the mental state called "nirvana." Meanwhile, the clock by the stove is measuring physical time and is not affected by a particular individual's consciousness. When a physicist defines speed to be the rate of change of position with respect to time, the term "time" refers to physical time. Physical time is more basic for helping us understand our shared experiences in the world, and so it is more useful than psychological time for doing science. But psychological time is vitally important for understanding many human thought processes. We even have a sense of the passage of time during our sleep, and we awake knowing we've slept for one night, not for one month. But if we've been under a general anesthetic and wake up, we have no sense of how long we've been unconscious. Psychological time stopped.
Psychologists are interested in whether we can speed our minds while slowing our psychological time. If so, we might become mentally more productive, get more high quality decision making done per fixed amount of physical time, learn more per minute. Several avenues have been explored: using drugs such as cocaine and amphetamines, undergoing extreme experiences such as jumping backwards off a tall tower with bungee cords attached to the legs, and trying different forms of meditation. So far, none of these avenues have led to success productivity-wise.
Any organism's sense of time is subjective, but is the time that is sensed also subjective, a mind-dependent phenomenon? If it were subjective in the way judgments of good food or good music are subjective, then it would be miraculous that everyone can so easily agree on the ordering of public events in time. For example, first, Einstein was born, then he went to school, then he died. Everybody agrees that it happened in this order: birth, school, death. No other order. The agreement on time order for so many phenomena is part of the reason that many philosophers and scientists believe physical time is an objective phenomenon not dependent on being consciously experienced. The other part of the reason time is believed to be objective is that our universe has a large number of different processes that bear consistent time relations, or frequency of occurrence relations, to each other. For example, the frequency of a fixed-length pendulum is a constant multiple of the half life of a specific radioactive uranium isotope; the relationship doesn't change as time goes by (at least not much and not for a long time). The existence of these sorts of relationships makes our system of physical laws much simpler than it otherwise would be, and it makes us more confident that there is something objective we are referring to with the time-variable in those laws.
If there were no minds, would physical time be absent, too? Aristotle raised this metaphysical question when he said, "Whether, if soul (mind) did not exist, time would exist or not, is a question that may fairly be asked; for if there cannot be someone to count there cannot be anything that can be counted..." [Physics, chapter 14]. He doesn't answer his own question because, he says rather profoundly, it depends on whether time is the conscious numbering of movement or instead is just the capability of movement's being numbered were consciousness to exist. Aristotle's distinction foreshadows the modern distinction between psychological time and physical time.
St. Augustine, adopting a subjective view of time, said time is nothing in reality but exists only in the mind's apprehension of that reality. Henry of Ghent and Giles of Rome both said time exists in reality as a mind-independent continuum, but is distinguished into earlier and later parts only by the mind. In the 11th century, the Persian philosopher Avicenna doubted the existence of physical time, arguing that time exists only in the mind due to memory and expectation. In the 13th century, Duns Scotus disagreed with all these philosophers and recognized both physical and psychological time.
At the end of the 18th century, Kant suggested a subtle relationship between time and mind--that our mind structures our perceptions so that we know a priori that time is like a mathematical line. Time is, on this theory, a form of conscious experience.
In the 20th century, the philosopher of science Bas van Fraassen described physical time by saying, "There would be no time were there no beings capable of reason" just as "there would be no food were there no organisms, and no teacups if there were no tea drinkers," and no cultural objects without a culture.
The controversy in metaphysics between idealism and realism is that, for the idealist, nothing exists independently of the mind. If this controversy is settled in favor of idealism, then time, too, would have that subjective feature--physical time as well as psychological time.
Another philosophical issue involving time and mind is how to account for our "feeling" that time passes, that it flows? Philosophers disagree about whether this flow is an objective feature of reality or is, instead, entirely a feature of human perception. In other words, does our mind contribute the flow to time? This is an issue even if it is agreed that time itself is objective. Within the field of cognitive science, one wants to know what are the neural mechanisms that account for our experience of time, but so far very little progress has been made on this fascinating topic.
It has been suggested by some philosophers that Einstein's theory of relativity, when confirmed, showed us that time depends on the observer, and thus that time is subjective, or dependent on the mind. This error is probably caused by Einstein's use of the term "observer." Einstein's theory does imply that the duration of an event isn't absolute but depends on the observer's frame of reference or coordinate system. But what Einstein means by "observer's frame of reference" is merely a perspective or framework from which measurements could be made. The "observer" does not have to be a conscious being or have a mind; it could be a clock on a rock. Einstein's point is that a clock on this rock might measure a different duration than a second clock in a rocket hurtling past the rock. Einstein isn't making a point about mind-dependence.
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3. What is time?
One way to answer the question "What is time?" is to declare that it is what accurate clocks measure. This is correct, but it doesn't tell us enough. We want something "deeper."
The most popular "deep" answer to the question "What is physical time?" is that it is a special system of relations among instantaneous events. It is what underlies our temporal claims that Newton lived before Einstein but at the same time as Leibniz yet a lot longer than anyone who died as a teenager. (The relations are in italics.) This is the answer offered by Adolf Grünbaum who applies the contemporary mathematical theory of continuity to physical processes. How do we tell whether this is the correct answer to our question? To be convinced, we need to be told what the relevant terms mean, such as "certain system of relations." In addition, we need to be presented with a theory of time implying that time is this system of relations; and we need to be shown how that theory adequately addresses the many features that are required for a successful theory of time. This article won't carry out this task.
A different answer to the question "What is time?" is that time is the form of becoming. To assess this answer, which is from Alfred North Whitehead, we need to be told what the term "form of becoming" means; we need to be presented with a detailed theory of time implying that time is the form of becoming; and we need to investigate how it addresses those many features required for a successful theory of time. The metaphysical attitude being used here in assessing whether Grünbaum's and Whitehead's answers are correct is the attitude that fruitful problem solving is a guide to what exists. It is the same attitude that declares zero to exist because zero is so useful for solving the numerical equation x + b = c in the special case when the two numbers b and c happen to be equal, and because having solutions to these sorts of equations is indispensable to the best scientific theories.
If physical time, psychological time, and biological time are three different kinds of time, then three answers are required to the question "What is time?" and some commentary is required regarding their relationships, such as whether one is the most fundamental. Many philosophers of science argue that physical time is the most fundamental of the three even though psychological time is discovered first by each of us as we grow out of our childhood, and even though psychological time was discovered first as we human beings evolved from our animal ancestors. The remainder of this article focuses more on physical time than psychological or biological time.
Another answer to "What is time?" is that time is whatever the time variable t is denoting in the best-confirmed and most fundamental theories of current science. Nearly all philosophers would complain that this answer is just saying the time variable ranges over times. The answer is methodologically suspect, they say, because the nature of physical time can be revealed only with a philosophical theory of time that addresses the many philosophical issues that scientists don't concern themselves with.
Some philosophers, notably Zeno and McTaggart, answer the question, "What is time?" by replying that it is nothing because it doesn't exist. In a similar vein, the early 20th century English philosopher F. H. Bradley argues, "Time, like space, has most evidently proved not to be real, but a contradictory appearance....The problem of change defies solution." However, most philosophers agree that time does exist. They just can't agree on what it is.
Whatever time is, it is not "time." One has four letters; the other does not. Nevertheless, it might help us understand time if we improved our understanding of the sense and reference of the word "time." Should the proper answer to the question "What is time?" produce a definition of the word as a means of capturing its sense? Definitely not--if the definition must be some analysis that provides a simple paraphrase in all its occurrences. There are just too many varied occurrences of the word: time out, behind the times, in the nick of time, and so forth.
But how about a definition that is more realistic? Might it be helpful to explore the grammar of the term "time" in either ordinary language or the physics literature? Most philosophers today would agree with A. N. Prior who remarked that, "there are genuine metaphysical problems, but I think you have to talk about grammar at least a little bit in order to solve most of them." However, do we learn enough about what time is when we learn about the grammatical intricacies of the word? Ordinary-language philosophers are especially interested in time talk, in what Wittgenstein called the "language game" of discourse about time. Wittgenstein's expectation is that by drawing attention to ordinary ways of speaking about time we will dissolve rather than answer our philosophical question. But most philosophers of time are unsatisfied with this approach and have the goal of uncovering important features about time itself.
That was Aristotle's goal when he provided an early, careful answer to our question, "What is time?" by declaring that time is the "number of movement in respect of the before and after, and is continuous.... In respect of size there is no minimum; for every line is divided ad infinitum. Hence it is so with time" [Physics, chapter 11]. Here he is focusing more on duration than on time itself. Although Aristotle did say "time is the measure of change" [Physics, chapter 12], he emphasizes "that time is not change [itself]" because a change "may be faster or slower, but not time..." [Physics, chapter 10]. For example, a specific change such as the descent of a leaf can be faster or slower, but time itself can't be faster or slower. Aristotle advocates what is now referred to as the relational theory of time because he believed that "there is no time apart from change...." [Physics, chapter 11].
René Descartes had a very different answer to "What is time?" He argued that a material body has the property of spatial extension but no inherent capacity for temporal endurance, and that God by his continual action recreates the body at each successive instant. Time, therefore, is a divine process of re-creation.
In the 17th century, the English physicist Isaac Barrow rejected Aristotle's linkage between time and change by saying that time is something which exists independently of motion or change and which existed even before God created the matter in the universe. Barrow's student, Isaac Newton, agreed that the relational theory of time is incorrect. Newton argued very specifically that time and space are an infinitely large container for all events, and that the container exists with or without the events. He added that space and time are not material substances, but are like substances in not being dependent on matter or motions or anything else except God.
Gottfried Leibniz objected. He argued that time is not an entity existing independently of actual events. He insisted that Newton had underemphasized the fact that time necessarily involves an ordering of any pair of non-simultaneous events. This is why time "needs" events, so to speak. Leibniz added that this overall order is time.
In the 18th century, Immanuel Kant said time and space are forms that the mind projects upon the external things-in-themselves. He spoke of our mind structuring our perceptions so that space always has a Euclidean geometry, and time has the structure of the mathematical line. Kant's idea that time is a form of apprehending phenomena is probably best taken as suggesting that we have no direct perception of time but only the ability to experience things and events in time. Some historians distinguish perceptual space from physical space and say that Kant was right about perceptual space. It's difficult, though, to get a clear concept of perceptual space. If physical space and perceptual space are the same thing, then Kant is claiming we know a priori that physical space is Euclidean. With the discovery of non-Euclidean geometries in the 1820s, and with increased doubt about the reliability of Kant's method of transcendental proof, the view that truths about space and time are apriori truths began to lose favor.
In 1924, Hans Reichenbach defined time order in terms of possible cause. Event A happens before event B if A could have caused B but B couldn't have caused A. This was the first causal theory of time, that was originally suggested by Leibniz who said, "If of two elements which are not simultaneous one comprehends the cause of the other, then the former is considered as preceding, the latter as succeeding." The usefulness of the causal theory depends on a clarification of the notorious notions of causality and possibility without producing a circular explanation that presupposes an understanding of time order. Reichenbach's idea was that causal order can be explained in terms of the "fork asymmetry". The asymmetry is due to the fact that outgoing processes from a common center tend to be correlated with one another, but incoming processes to a common center are uncorrelated. [Do you remember tossing a rock into a still pond? Imagine what the initial conditions at the edge of a pond must be like to produce correlated, incoming, concentric water waves that would expel the rock and leave the water surface smooth.] Some philosophers argue that temporal asymmetry, but not temporal priority, can be analyzed in terms of causation. But even if Reichenbach were correct that temporal priority can be analyzed in terms of causation, the question remains whether time itself can be analyzed in those terms.
The usefulness of the causal theory also depends on a refutation of David Hume's view that causation is simply a matter of constant conjunction [that is, always being together]. For Hume, there is nothing metaphysically deep about causes preceding their effects; it's just a matter of convention that we use the terms "cause" and "effect" to distinguish the earlier and later members of a pair of events which are related by constant conjunction.
During history, a variety of answers have been given to the question of whether time is like a line or, instead, like a circle. The concept of linear time first appeared in the writings of the Hebrews and the Zoroastrian Iranians. The Roman writer Seneca also advocated linear time. Plato and and most other Greeks and Romans believed time to be motion and believed cosmic motion was cyclical, but this wasn't envisioned as requiring any detailed endless repetition such as the multiple rebirths of Socrates. However, the Pythagoreans and some Stoic philosophers did adopt this drastic position.
With circular time, you can be assured that after your death you will be reborn. The future will become the past. If time is like this, then the question arises as to whether there would be an endless number of times when each state of the world reoccurred, or whether, accepting Leibniz's Principle of the Identity of Indiscernibles, each supposedly repeating state of the world would occur just once because each state would be not be discernible from the repeated state.
Islamic and Christian theologians adopted the Greek common sense idea that time is linear and the Jewish-Zoroastrian idea that the universe was created at a definite moment in the past. Augustine emphasized that human experience is a one-way journey from Genesis to Judgment, regardless of any recurring patterns or cycles in nature. In the Medieval period, Thomas Aquinas agreed. Nevertheless, it was not until 1602 that the concept of linear time was more clearly formulated--by the English philosopher Francis Bacon. In 1687, Newton advocated linear time when he represented time mathematically by using a line rather than a circle. The concept of linear time was promoted by Barrow, Leibniz, Locke and Kant. In 19th century Europe, the idea of linear time became dominant in both science and philosophy. However, in the twentieth century, Gödel and others discovered solutions to the equations of Einstein's general theory of relativity that allowed closed loops of proper time. These causal loops or closed curves in spacetime allow you to go forward continuously in time until you arrive back into your past. You might even meet your younger self. If so, some definitions of "person" will need to be revised to allow for this. The logic of the term "time" that is embedded in our time talk does not rule out a nonlinear structure for time, but there is no reason to believe (physical) time is actually like this or that anything has gone back in time.
Is time an emergent entity? Sound emerges from molecules in the sense that, although a single molecule can have no sound, a very large group of molecules can make a sound. Does time emerge from more basic entities? There are two opposing camps on this issue. One says that both space and time emerge from some micro-substrate, although there is no agreed upon theory of what the substrate is. The second camp says that space emerges but time does not. In 2004, after winning the Nobel Prize in physics, David Gross expressed the views of this second camp:
Everyone in string theory is convinced...that spacetime is doomed. But we don't know what it's replaced by. We have enormous amount of evidence that space is doomed. We even have examples, mathematically well-defined examples, where space is an emergent concept.... But in my opinion the tough problem that has not yet been faced up to at all is, "How do we imagine a dynamical theory of physics in which time is emergent?" ...All the examples we have do not have an emergent time. They have emergent space but not time. It is very hard for me to imagine a formulation of physics without time as a primary concept because physics is typically thought of as predicting the future given the past. We have unitary time evolution. How could we have a theory of physics where we start with something in which time is never mentioned?
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4. What does science require of time?
a. Relativity and Quantum Mechanics
The general theory of relativity and quantum mechanics are the two most fundamental theories of physics, and the Big Bang theory is the leading theory of cosmology. According to relativity and quantum mechanics, spacetime is, loosely speaking, a collection of points called "spacetime locations" where the universe's physical events occur. Spacetime is four-dimensional and a continuum, and time is a distinguished, one-dimensional sub-space of this continuum. Any interval of time--any duration--must be a linear continuum of instants in which one event follows another from past to present to future. So, a duration has a structure like an interval of real numbers. General relativity theory allows the geometry of space to change with time as the distribution of matter-energy changes.
This first response to the question "What does science require of time?" is too simple. There are complications. There is an important difference between the universe's cosmic time and a clock's proper time; and there is an important difference between proper time and a reference frame's coordinate time. Most spacetimes can not have coordinate systems. Our theory of cosmology, which is some version of the Big Bang theory, places additional requirements on time, as we shall see in the next section. Some physicists are advocating revision of the classical Big Bang theory in order to allow for the "multiverse," in which there are multiple Big Bangs in parallel universes, so that there is time before our Big Bang. Also, all physicists believe that relativity and quantum mechanics are logically inconsistent and need to be replaced by a theory of quantum gravity. A theory of quantum gravity is likely to have radical implications for our understanding of time, such as time and space losing their discreteness and even their separate identities on the very smallest scale.
Aristotle, Leibniz, Newton, and everyone else before Einstein, believed there was a frame-independent duration between two events. For example, if the time interval between two lightning flashes is 100 seconds on someone's accurate clock, then the interval also is 100 seconds on your accurate clock, even if you are flying by at an incredible speed. Einstein rejected this piece of common sense in his 1905 special theory of relativity when he declared that the time interval between two events depends on the observer's reference frame. As Einstein expressed it, "Every reference-body has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event." Each reference frame, or reference-body, divides spacetime differently into its time part and its space part.
In 1908, the mathematician Hermann Minkowski had an original idea in metaphysics regarding space and time. He was the first person to realize that spacetime is more fundamental than time or space alone. As he put it, "Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality." The metaphysical assumption behind Minkowski's remark is that what is "independently real" is what does not vary from one reference frame to another. It's their "union," what we now call "spacetime," that doesn't vary. It follows that the division of events into the past ones, the present ones, and the future ones is also not "independently real". However, space and time are not completely equivalent even in relativity because time is a "distinguished" sub-space of the 4-d spacetime continuum. Being distinguished implies that time isn't just another 4th dimension of physical space; it's a special dimension unlike the space dimensions, even when we confine our attention to a single reference frame.
A coordinate system is a way of representing space and time using numbers to represent spacetime points. Science confidently assigns numbers to times because, in any reference frame, the happens-before order-relation on events is faithfully reflected in the less-than order-relation on the time numbers (dates) that we assign to events. In the fundamental theories such as relativity and quantum mechanics, the values of the time variable t are real numbers, not merely rational numbers. Each number designates an instant of time, and time is a linear continuum of these instants, similar to the mathematician's line segment. Therefore, if these fundamental theories are correct, physical time is one-dimensional rather than two-dimensional, and continuous rather than discrete. These features don't require time to be linear, however, because a segment of a circle is also a linear continuum, but there is no evidence for circular time, that is, for causal loops or worldlines that are closed curves in spacetime.
What about instants? A duration is an ordered set of instants, not a whole or sum of instants. That is, instants are members of durations, not parts of them. Any duration is infinitely divisible, and it endlessly divides into more intervals; it never divides into instants. The parts of durations are just more durations. The instant is not part of the duration; instead, the singleton set of an instant is a subset of the duration. Instants are like real numbers in that they are boundaries of durations. They are locations in time, but they are "in" time as members are in sets, not as parts are in wholes.
Regarding the number of instants in a duration, time's being a linear continuum implies the instants are so densely packed that between any two there is a third, so that no instant has a next instant. In fact, time's being a linear continuum implies that there is a nondenumerable infinity of instants between any two instants. There is little doubt that the actual temporal structure of events can be embedded in the real numbers, but how about the converse? That is, to what extent is it known that the real numbers can be adequately embedded into the structure of the instants? The problem is that, although time is not quantized in quantum theory, for times shorter than about 10-43 seconds, the so-called Planck time, science has no experimental grounds for the claim that between any two events there is a third. Instead, the justification is that the assumption of continuity is convenient and useful, and that there are no better theories available.
Because of quantum mechanical considerations, physicists agree that the general theory of relativity must fail for durations shorter than the Planck time, but they don't know just how it fails. Most importantly here, there is no agreement among physicists as to whether the continuum feature of time will be adopted in the future theory of quantum gravity that will be created to take account of both gravitational and quantum phenomena. The string theory of quantum gravity predicts that time is continuous, but an alternative to string theory, loop quantum gravity, does not.
Relativity theory challenges a great many of our intuitive beliefs about time. The theory is inconsistent with the common belief that the temporal order in which two events occur is independent of the observer's point of reference. For events occurring at the same place, relativity theory implies the order is absolute (independent of the frame), but for distant events occurring close enough in time to be in each other's absolute elsewhere, event A can occur before event B in one reference frame, but after B in another frame, and simultaneously with B in yet another frame.
Science impacts our understanding of time in many other fundamental ways. Relativity theory implies there is time dilation between one frame and another. For example, the faster a clock moves, the slower it runs, relative to stationary clocks. Time dilation shows itself when a speeding twin returns to find that his (or her) Earth-bound twin has aged more rapidly. This surprising dilation result has caused some philosophers to question the consistency of relativity theory, arguing that, if motion is relative, then from the perspective of the speeding twin, the speeding twin should, instead, be the one who aged more rapidly. This argument is called the twins paradox. Experts now are agreed that the mistake is within the argument for the paradox, not within relativity theory. As is shown in more detail in the Supplement of Frequently Asked Questions, the argument fails to notice the radically different relationships that each twin has to the rest of the universe as a whole.
There are two kinds of time dilation. Special relativity's time dilation involves speed; general relativity's involves acceleration and gravitational fields. Two ideally synchronized clocks need not stay in synchrony if they undergo different accelerations or different gravitational forces. We've already mentioned the clock that is taken to the wine cellar. This gravitational time dilation would be especially apparent if one of the two clocks were to fall into a black hole. A black hole can form when a star exhausts its nuclear fuel and contracts so compactly that the gravitational force prevents anything from escaping the hole, even light itself. The envelope of no return surrounding the black hole is its event horizon. As a clock falls toward a black hole, time slows on approach to the event horizon, and it completely stops at the horizon (not just at the center of the hole)--relative to time on a clock that remains safely back on Earth.
General Relativity theory may have even more profound implications for time. In 1948, the logician Kurt Gödel discovered radical solutions to Einstein's equations, solutions in which there are closed timelike curves, so that as one progresses forward in time along one of these curves one arrives back at one's starting point. Gödel drew the conclusion that in such a universe, there cannot be "an objective lapse of time." So, "whether or not an objective lapse of time exists," that is, whether time really exists, depends "on the particular way in which matter and its motion are arranged in the world." If matter is distributed so that there is Gödelian spacetime, then the universe has no time. Reinforcing this conclusion, Stephen Hawking showed in 1969 that only if a general relativistic spacetime fails to have closed timelike curves can it admit of a partition into spacelike 3-d slices.
In Einstein's relativity theory, the focus is on proper time rather than a global, coordinate time. Proper time along a worldline in 4-d spacetime is the time elapsed by an object having that worldline, as shown on an ideal clock having the same worldline. According to the relationist, what it is that is being measured when we measure proper time? If the object being measured never changes, then we aren't measuring change in the object. The standard answer is that we are measuring the advancing phase of the quantum wave function, an esoteric kind of change.
b. The Big Bang
In 1922, the Russian physicist Alexander Friedmann predicted from general relativity that the universe should be expanding. In 1927, the Belgian physicist Georges Lemaitre suggested that galaxy movement could best be accounted for by this expansion. And in 1929, the American astronomer Edwin Hubble made careful observations of clusters of galaxies and confirmed that the universe is undergoing a universal expansion. Atoms are not expanding; our solar system is not expanding; even the cluster of galaxies to which the Milky Way belongs is not expanding. But most every galaxy cluster is moving away from the others. It's as if the clusters are exploding away from each other, and in the future they will be very much farther away from each other. Now, consider the past instead of the future. At any earlier moment the universe was more compact. Projecting to earlier and earlier times, and assuming that gravitation is the main force at work, the astronomers now conclude that 13.7 billion years ago (plus or minus 1%) the universe was in a state of nearly zero size and infinite density. Because all substances cool when they expand, physicists believe the universe itself must have been cooling down over the last 13.7 billion years, and so it begin expanding when it was extremely hot. The Big Bang theory is a theory of how our universe evolved, how it expanded and cooled from this beginning. This beginning process is called the "Big Bang." As far as we knew back in the 20th century, the entire universe was created in the Big Bang, and time itself came into existence "at that time." So, asking what happened before the Big Bang was like asking what on Earth is north of the North Pole. At least that's the best response to this question assuming the classical theory of the Big Bang of the 20th century. With the appearance of the new theories of quantum gravity and the multiverse in the 21st century, the question has been resurrected as legitimate.
In the literature in both physics and philosophy, descriptions of the Big Bang often assume that a first event is also a first instant of time and that spacetime did not exist outside the Big Bang. This intimate linking of a first event with a first time is a philosophical move, not something demanded by the science. It is not even clear that it's correct to call the Big Bang an event. The Big Bang "event" is a singularity without space coordinates, but events normally must have space coordinates. One response to this problem is to alter the definition of "event" to allow the Big Bang to be an event. Another response, from James Hartle and Stephen Hawking, is to consider the past cosmic time-interval to be open rather than closed at t = 0. Looking back to the Big Bang is then like following the positive real numbers back to ever smaller positive numbers without ever reaching a smallest positive one. If Hartle and Hawking are correct that time is actually like this, then the universe had no beginning event, but it has a finite amount of past time, and the term "the Big Bang" refers not to any single event. But in order to simplify the discussion ahead, this article will speak of "the" Big Bang event as if it were a single event. The Big Bang theory in some form or other is accepted by the vast majority of astronomers, but it is not as firmly accepted as is the theory of relativity.
There are serious difficulties in defending the Big Bang theory's implications about the universe's beginning and the universe's future. Classical Big Bang theory is based on the assumption that the universal expansion of clusters of galaxies can be projected all the way back. Yet physicists agree that the projection must fail in the Planck era, that is, for all times less than 10-43 seconds after "the" Big Bang. Therefore, current science cannot speak with confidence about the nature of time within the Planck era. If a theory of quantum gravity does get confirmed, it should provide information about the Planck era, and it may even allow physicists to answer the question, "What caused the Big Bang?" The scientifically radical, but theologically popular, answer, "God caused the Big Bang, but He, himself, does not exist in time" is a cryptic answer because it is not based on a well-justified and detailed theory of who God is, how He caused the Big Bang, and how He can exist but not be in time. It is also difficult to understand St. Augustine's remark that "time itself was made by God." On the other hand, for a person of faith, belief in God as creator is usually stronger than belief in any scientific hypothesis or in any epistemological desire for a scientific justification of the remark about God or in the importance of satisfying any philosopher's demand for clarification.
Careful cosmological observations near the end of the 20th century and beginning of the 21st have now convinced astrophysicists that the volume of space is not finite, but is infinite and by-and-large flat. Its large scale geometry is Euclidean, not Riemannian nor hyperbolic. Since 2000, many cosmologists have come to believe the Big Bang wasn't the beginning after all, and the universe was infinite even when our Big Bang was initiating. This has fueled theories of the multiverse. The multiverse contains other universes much like our universe, except that they are very far away from ours. Although the theory hasn't been tested, the key idea here is that if spacetime is infinite, then everything that is possible is actual somewhere. Since there are different possible initial values at the time of our Big Bang, there must be different kinds of Big Bangs that have taken place elsewhere at different times [before and after our Big Bang]. These other Big Bangs have created "parallel" universes. Ascending another level up the hierarchy of multiverses, if there are different possible values for the physical constants and for the kinds of elementary particles in our universe, then there must be parallel universes far from us which have all those possible values. To ascend yet again, if, according to quantum mechanics, at any instant in a universe, there are alternative possibilities for what event occurs next, then there must be parallel universes in which all those possibilities are actualities, though these universes won't be far away, but will be truly parallel in the sense of being off in their own space. Finally, progressing again up the hierarchy of speculation about multiverses, if there are various logically possible alternatives for the laws of physics, then every such logically possible universe is an actual universe, and we have something very similar to the modal realism of the Princeton philosopher David Lewis. [See Tegmark 2003.] In some of these universes there is no time dimension.
c. Is time infinite?
There are three ways to interpret the question of whether physical time is infinite: (a) Was there an infinite amount of time in the universe's past? (b) Is time infinitely divisible? (c) Will there be an infinite amount of time in the future?
(a) Was there an infinite amount of time in the past? By invoking the radical notion that God is "outside of time," St. Augustine declared, "Time itself being part of God's creation, there was simply no before!" So, for theological reasons, Augustine declared time had a finite past. After advances in astronomy in the late 19th and early 20th centuries, the question of the age of the universe became a scientific question. With the acceptance of the classical Big Bang theory, the amount of past time was judged to be less than 14 billion years because this is when the Big Bang began. The assumption is that time does not exist independently of the spacetime relations exhibited by physical events. Recently, however, the classical Big Bang theory has been challenged. There could be an infinite amount of time in the past according to some proposed, but as yet untested, theories of quantum gravity based on the assumptions that general relativity theory fails to hold for infinitesimal volumes. These theories imply that the beginning of the Big Bang was actually an expansion from a pre-existing physical state. There was never a singularity. In that case our Big Bang could be just one bang among other bangs throughout an infinite past of the multiverse. For a discussion of these theories requiring an infinite past time, see Veneziano, 2004.
(b) Is time infinitely divisible? Yes, because general relativity and quantum mechanics require time to be a continuum. But the answer is no if these theories are eventually replaced by a relativistic quantum mechanics that quantizes time. Several untested theories presupposes a discrete, rather than a continuous time.
(c) Will there be an infinite amount of time in the future? Probably. According to the classical theory of the Big Bang, the answer depends on whether events will keep occurring. The best estimate from the cosmologists these days is that the expansion of the universe is accelerating and will continue forever. There always will be the events of galaxies getting farther apart, and so time will have an infinite duration in the future, even though gravity will continue to compact much of the matter into black holes.
There have been interesting speculations on how conscious life could continue forever, despite the fact that the available energy for life will decrease as the universe expands, and despite the fact that any life swept up into a black hole will reach the center of the hole in a finite time at which point death will be certain. For an introduction to these speculations, see Krauss and Starkman, 2002.
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d. Atoms of time
In the classical theories of relativity and quantum mechanics, time is not quantized, but is a continuum having the character described above. However, if certain, as yet untested, theories attempting to unify relativity and quantum mechanics are correct--such as the theory of loop quantum gravity--then time will come in discrete pieces or atoms lasting about 10-43 second. There will be a shortest duration for any possible event, and time will be "digital" rather than "analog."
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5. What kinds of time travel are possible?
The term "time travel" is a metaphor because the ordinary term "travel" implies change in spatial location, but the term "time travel" implies change in "temporal location." There are many phenomena that have been taken by some people to be time travel [crossing a time zone, being frozen, remembering past events] but which are not now under serious consideration by philosophers of time, so this section does not focus on them. Using the term "time travel" in the sense that is of interest today to philosophers of time, there is travel to the past and travel to the future.
a. Travel to the future
According to relativity theory, there are two ways to travel into another person's future. First, in the twins paradox, a person speeding away from their twin who remains on Earth will, upon reunion, be younger than their two who stayed back on Earth. The speeding twin will have traveled in time, relative to the proper time of the Earth-based twin. For a second type of forward time travel, if a twin goes to a stronger gravitational field by leaving the dinner table and descending to the cellar for a bottle of wine and then returns, he (or she) will have entered the future of the twin who stayed at the dinner table. When someone enters a relatively stronger gravitational field, the person's physical time slows down relative to the time of those who do not enter the stronger field. That's why it takes a potentially infinite amount of our proper Earth time for something to fall into a black hole.
Regarding the first way to travel to the future, if you have a fast enough spaceship, you can travel to the year 4,500 A.D. on Earth. You can affect that future, not just see it. This is a direct consequence of the time dilation described in the theory of relativity. You can travel to someone else's future, not your own. You're always in your own present. Unfortunately, once you go to 4,500 A.D. (as judged in a frame of reference in which the Earth is considered stationary), you are stuck in the Earth's future. You can not reverse course in your spaceship and return to the 21st century on Earth. You must live with the consequence that all your friends have died centuries ago.
On this trip to 4,500 A.D., how much time would elapse on your own clock? The answer depends on how fast your spaceship goes, what accelerations occur, and what gravitational forces are acting. The faster your spaceship goes, the less time it will take--actually take, not just appear to take. As you approach infinitesimally close to the speed of light, the trip to 4,500 A.D. will take essentially no time at all. That's from your own perspective though; observers who remained stationary on Earth and judged your flight from their perspective will have observed you for thousands of years.
Regarding the second way to travel to the future, if your spaceship could travel "very" close to the surface of a black hole and then return, you could land back on Earth in the year 4,500 A.D. with your wristwatch showing accurately that you'd been gone only a few years.
The two types of time travel to the future have been carefully tested, though not for spaceships, and all physicists agree that they occur as described by relativity theory. However, in science fiction movies, which almost always depict nonrelativistic time travel, time travelers suddenly appear from out of the past or out of the future, and other travelers suddenly disappear from now and pop into the past or the future. These phenomena of sudden appearance have never been observed reliably, despite the literature in parapsychology. If they were reliably observed, then we might very well consider accepting the hypothesis that spacetime has an extra dimension allowing time travel. The traveler's discontinuous worldline in ordinary 4-d spacetime could actually be a continuous worldline in 5-d spacetime, permitting a "sudden appearance" in our 4-d spacetime.
b. Travel to the past
Special relativity does not permit time travel to the past. Actually this isn't an accurate statement. Special relativity permits tachyons, namely, particles that spend their lives moving faster than the speed of light, and these could go back in time, but there is no evidence that these exist. So, for ordinary particles that are going less than the speed of light, special relativity rules out travel to the past. However, general relativity permits this kind of time travel.
Let's suppose you do go back to the past, using a time machine which might just be an appropriately moving spaceship. One assumption made in the analysis of time travel is that the world is never logically contradictory. This is the heart of the Grandfather Paradox. According to this paradox, you step into a time machine, go back and kill your grandfather before he's met your grandmother, so you prevent your own birth. Therefore, you were both born and not born. That is logically contradictory. So, we may conclude that we erred in assuming the possibility of this sort of time travel. If time travel is going to exist, it can't permit any change in what is known to have happened.
How about influencing history instead of changing it? That is allowed. The time traveler helps make history what it was. For example, Joe Stalin, the dictator of Russia, was 21 years old in 1900. Let's suppose time machines are invented in 2080. In that year, Sam decides to assume the identity of Stalin. He knows Russian history, speaks fluent Russian, is 21 years old, and looks and acts like Joe Stalin did at 21. Sam enters the newly invented time machine, goes back to 1900, secretly murders Stalin, then starts calling himself "Stalin". Sam never reveals his past [as Sam, or never remembers it after entering the time machine], and he eventually becomes the dictator of Russia.
Because Stalin really died in 1953, Sam must die in 1953, many years before he is born. So, Sam's worldline will be composed of discontinuous segments. Events in 2080 will cause some events back in 1900. The worldlines of more continuous time travelers might instead be a loop, a closed timelike curve. Either possibility implies backward causation. Some philosophers believe backward causation can be ruled out by the definition of "cause," just as they can rule out Monday ever immediately following Friday. Other philosophers disagree on the grounds that backward causation should be considered merely improbable, not impossible.
Some philosophers believe Sam's time travel can be ruled out because of its inconsistency with our normal assumption that people are born before they die, never after they die, but most philosophers believe that the normal assumption can be revised with no harm.
Another implication of Sam's time travel that influences the past is his apparent violation of the law of conservation of matter by popping into existence in 1900. Must we also revise that law? The modern version of the law of conservation of matter-energy is that the conservation is statistical; matter is conserved on average. The shorter the time span and the smaller the mass involved then the more likely that there can be violations in conservation.
There are other significant implications involved with this sort of participatory time traveling—traveling back in time to participate in what actually happened. The future is oddly constrained by the time travel. After Sam arrives in Russia in 1900, the world's events must allow Sam at age 21 to enter the time machine. Nothing can happen to prevent Sam getting to the machine. All his enemies somehow must "botch" their attempts to kill him in 2079. Attempted sabotage of the time machine must also fail. Scientists viewing these attempts will be surprised that the saboteurs are continually yet inexplicably frustrated by unfavorable circumstances. Looking back from the year 2080, it will appear as if the world conspired to ensure that a predestined event occurred. It has been argued that because we've never seen the world conspire with massive coincidences, this kind of time travel never occurs even if it is logically and conceptually possible.
An additional argument against time travel of the kind that influences past events but doesn't change them is that by now we should have seen all sorts of time traveler tourists from the distant future. "A possible way to explain the absence of visitors from the future," says Stephen Hawking, "would be to say that the past is fixed because we have observed it and seen that it does not have the kind of warping needed to allow travel back from the future." One counterargument is that there might be very good reasons why our time hasn't yet been visited. The travelers might be uninterested in us, or it might be very expensive to go to our time. Or the travelers might already be here but be invisibly cloaked so as not to interfere with us. Therefore, it is jumping to conclusions to be so pessimistic about the probability of time travel.
Admittedly, though, no one has any practical and realistic plans for how to build a time machine. The worst plans begin in science fiction by saying, "First, suspend the laws of science. Then...." The best plans conform to today's scientific laws but use such phrases as "First, take a wormhole and...." W. J. van Stockum found the first solution to the equations of general relativity that permits a physical object to travel at less than the speed of light and yet arrive at its own past. Suppose someone orbits around a very rapidly spinning cylinder that is infinitely long. The proper time line of the orbiting space traveler can form a closed curve in spacetime. Since Stockum's initial, relatively unnoticed work in 1937, Kurt Gödel in 1948 found the second solution to the equations of general relativity that permit time travel to the past. Frank Tipler found another in 1974. Mathematical physicists have subsequently described even more time machines using wormholes, which are tunnels from one part of space to another. These apparently are consistent with Einstein's equations of general relativity, but they require what mathematicians call a multiply-connected space. For example, you can fall for a few seconds down a wormhole and pop out in a nearby galaxy. With a clever arrangement of the wormhole, you can get back to where you started but before you started--though not to a time before the wormhole was built.
General relativity theory is so complex that it isn't always clear, even to the experts, what is and isn't allowed by the theory. Other physicists accept that Einstein's equations do allow backward time travel, but they rule out these solutions as being physically impossible or improbable for other reasons, such as there being no infinitely long, rapidly spinning cylinder available, or no wormholes. Einstein himself died believing that time travel to the past is impossible even if Gödel's scenario is consistent with his theory of relativity.
Maybe time travel is impossible because it allows the gaining of information for free. Print out this article that you are reading. Enter a time machine with it, and give it to me before I ever thought about time travel. I then copy down the article and publish it in this encyclopedia. In response to puzzles like this, the Oxford physicist David Deutsch says nature must have some principle that outlaws getting free information. (Deutsch, 1994)
Probing the possibility of a contradiction in backwards time travel, John Earman has described a rocket ship that carries a very special time machine. The time machine is capable of firing one probe into its own past. Suppose the ship is programmed to fire the probe on a certain date unless a safety switch is on. Suppose the safety switch is programmed to be turned on if and only if the "return" or "impending arrival" of the probe is (or has been) detected by a sensing device on the ship. Does the probe get launched? It is launched if and only if it is not launched. The way out of Earman's paradox seems to require us to accept that (a) the universe conspires to keep people from building the probe or the safety switch or an effective sensing device, or (b) time travel probes must go so far back in time that they never survive and make it back to the time when they were launched, or (c) time travel into the past is impossible.
Feynman diagrams in particle physics were described by Feynman himself as illustrating how a particle's moving forward in time is actually its antiparticle moving backward in time. However, physicists don't take Feynman's suggestion literally. As a leading particle theorist, Chris Quigg of Fermi National Accelerator Laboratory, explained, "It's not that antiparticles in my laboratory are actually moving backward in time. What's really meant by that is that if I think of a particle moving from one place to another forward in time, the physical process is the same as it would be if we imagine running the film backward and also changing the particle into an antiparticle."
In addition to time travel that changes the past and time travel that participates in the past, consider a third kind, time travel that reaches the past of a different universe. This idea appeals to an unusual interpretation of quantum mechanics, the parallel universes interpretation. According to this interpretation, everything that can happen does happen in some universe or other. There's a universe in which the Nazis won World War II and Stalin was assassinated. There's another universe in which the Nazis won World War II and Stalin escaped all assassination attempts. On this theory of time travel, for you to travel back in time and have lunch with President Abraham Lincoln is for you to stop existing in the present universe as you enter the time machine and for you to appear earlier in time in a parallel universe, one in which you in fact did have lunch with Abraham Lincoln. This parallel worlds theory implies that we must change our current view of what makes a person the same person through time [say, bodily identity and continuity of consciousness through time in a single universe] and accept some kind of trans-universe personal identity.
For more discussion of time travel, see the article "Time Travel" elsewhere in this Encyclopedia.
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6. Is the relational theory of time preferable to the absolute theory?
Absolute theories are theories that imply time exists independently of the spacetime relations exhibited by physical events. Relational theories imply it does not. Some absolute theories describe spacetime as being like a container for events. The container exists with or without events in it. Relational theories imply there is no container without contents. John Norton's metaphors might help. Absolute spacetime is like a painter's canvas. Take away the paint (spacetime events) from the painting and you still have the canvas left. Relational spacetime is like citizenship. Take away the citizens (spacetime events), and you have no citizenship left.
Everyone agrees time cannot be measured without there being objects and changes, but the present issue is whether it exists without objects and changes. The absolute theories are theories that spacetime could exist even if there were no physical objects and events in the universe, but relational theories imply that spacetime is nothing but objects, their events, and the spatiotemporal relationships among them.
There are two senses of "absolute" that need to be distinguished. As we are using the term, it means independent of the events. A second sense of "absolute" means independent of observer or reference frame. Einstein's theory implies there is no absolute time in this second sense. Aristotle accepted absolute time in this second sense, but he rejected it in our sense of being independent of events. Instead, Aristotle took the relationalist position that, "neither does time exist without change [Physics, 218b]."
However, the battle lines were most clearly drawn in the early 18th century when Leibniz argued for the relationalist position against Newton, who had adopted an absolute theory of time. Leibniz's principal argument against Newton is a reductio ad absurdum. Suppose Newton's absolute space and time do exist. Then space would surely be the same in every place and every direction and every time. But one could then imagine a universe just like ours except with everything shifted five miles east and five minutes earlier. But there'd be no reason why this shifted universe does not exist and ours does. Now we've arrived at a contradiction. If there's no reason, then we have violated Leibniz's Principle of Sufficient Reason: that there is an understandable reason for everything being the way it is. So, Newton's absolute space and time do not exist. In short, the trouble with Newton's absolutism is that it leads to too many unnecessary possibilities.
Newton offered this two-part response: (1) Leibniz is correct to accept the Principle of Sufficient Reason regarding the rational intelligibility of the universe. But there don't have to be knowable reasons for humans; God might have had His own sufficient reason for creating the universe at a given place and time even though mere mortals cannot comprehend His reasons. Newton's second argument, the non-theological one, is now generally considered to be the more effective of the two. (2) The bucket thought-experiment shows that acceleration relative to absolute space is detectable; thus absolute space is real, and if absolute space is real, so it absolute time. Here are the details. Tie a bucket to a rope hanging from a tree. Partially fill the bucket with water, and let it come to equilibrium. Notice that there's no relative motion between the bucket and the water, and the water surface is flat. Now spin the bucket until the angular velocity of the water and the bucket are the same. Again there will be no relative motion between the bucket and the water, but now the water surface is concave. Because we can disregard the rest of the environment, and because all the bucket-to-water relations are the same, says Newton, the only explanation of the difference in surface shape must be that in the first case there's no motion relative to space but in the latter case there is. That is, absolute space is acting on the water surface when it spins. Alternatively expressed, the key idea is that the presence of centrifugal force is a sign of rotation relative to absolute space. Leibniz's theory cannot offer this absolutist explanation, but Leibniz could offer no better explanation. So, for many years thereafter, Newton's absolute theory of space and time was generally accepted by European scientists and philosophers.
One hundred years later, Kant entered the arena on the side of Newton. In a space containing only a single glove, Leibniz couldn't account for its being a right glove versus a left glove because all the internal relationships would be the same. However, we all know that there is a difference between a right and a left glove, so this difference is due to the glove's relationship to space itself. But if there is a "space itself," then Newton is correct.
Newton's absolute theory of time was dominant in the 18th and 19th centuries, even though during those centuries Huygens, Berkeley, and Mach had entered the arena on the side of Leibniz. In the 20th century, Reichenbach and the early Einstein declared the special theory of relativity to be a victory for the relational theory. Special relativity, they said, ruled out a space-filling aether, the leading candidate for absolute space, so the absolute theory was incorrect. And the response to Newton's bucket argument is to note Newton's error in not considering the environment. According to general relativity, if you hold the bucket still but spin the background stars, the water will creep up the side of the bucket.
However, some philosophers argued that Reichenbach and the early Einstein may have been overstating the amount of metaphysics that can be extracted from the physics. Remember the ambiguity in "absolute" mentioned above? There is absolute in the sense of independent of reference frame and absolute in the sense of independent of events. Which sense is ruled out when we reject a space-filling aether? The critics of Reichenbach and the early Einstein admit that relativity theory does provide an effective response to Newton's bucket experiment, which was a classical thought experiment favoring the absolute theory. And they admit that general relativity does show that the curvature of spacetime is affected by the distribution of matter, so today it is no longer plausible for an absolutist to assert that the "container" is independent of the matter it contains. But, they argue, general relativity doesn't rule out a more sophisticated absolute theory. By the end of the 20th century, absolute theories had gained some ground thanks to the arguments of Adolf Grünbaum, John Earman and Michael Friedman.
In 1969, Sydney Shoemaker presented an argument to convince us of the understandability of time existing without change, as Newton's absolutism requires. Divide space into three disjoint regions, called region 3, region 4, and region 5. In region 3, change ceases every third year for one year. People in regions 4 and 5 can verify this and convince the people in region 3 after they come back to life at the end of their frozen year. Similarly, change ceases in region 4 every fourth year for a year; and change ceases in region 5 every fifth year. Every sixty years, that is, every 3 x 4 x 5 years, all three regions freeze simultaneously for a year. In year sixty-one, everyone comes back to life, time having marched on for a year with no change. But philosophers of time argued that even if time's existing without change is understandable, the deeper question is whether time does exist without change.
Here is one argument for absolutism. There can be no "empty" time, the relationist says. If events occur in a room before 11:01 AM and after 11:01 AM, but not exactly at 11:01 AM, must the relationist say there never was a time of 11:01 AM in the room? No relationist wants to answer, "yes." One relationist response is to say 11:01 exists in the room and everywhere else because somewhere outside the room something is happening then, and somehow or other sense can be made of time in the room in terms of these external events. The absolute will ask us to consider the possibility that the room is the whole universe. Then the relationist response to losing 11:01 AM would be to say possible events occur then in the room even if actual events do not. If the relational theory were to consider spacetime points to be permanent possibilities of the location of events, then the relationist theory would collapse into substantivalism, and there would no longer be a difference between the two theories. To the absolutist, a spacetime point is also just a place where something could happen.
Hartry Field argues for the absolute theory by pointing out that modern physics requires gravitational and electromagnetic fields that cover spacetime. They are states of spacetime. These fields cannot be states of some Newtonian aether, but there must be something to have the field properties. What else except substantive spacetime points?
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7. Does time flow?
"It is as if we were floating on a river, carried by the current past the manifold of events which is spread out timelessly on the bank," said Plato. Santayana offered another metaphor: "The essence of nowness runs like fire along the fuse of time." The philosopher's goal is to clarify the metaphor of time's flow. Everyone agrees that the passage of time "appears" to us humans to flow, although few believe that all conscious beings, say crocodiles, recognize the flow. Even if time does flow, there is the additional question of whether the flow can change. Can time's flow be slower on Friday afternoon?
There have been three major theories of time's flow. The first, and most popular among physicists, is that the flow is an illusion, the product of a faulty metaphor. The second theory is that it is not an illusion but rather is subjective, being deeply ingrained due to the nature of our minds. The third is that it is objective, a feature of the mind-independent reality that is to be found in, say, today scientific laws, or, if it has been missed there, then in future scientific laws. The third theory is often called the "dynamic theory" of time, and a popular synonym for the "flow of time" is "temporal becoming." Some dynamic theorists argue that the boundary separating the future from the past is the moment at which that which was undetermined becomes determined, and so "becoming" has the same meaning as "becoming determined."
Is the passage of time a feature of the world to be explained by noting how events change? Do events, as they cross the boundary of the present, lose their property of being indeterminate, or lose their property of futurity [McTaggart's theory], or gain some other property, and doesn't this explain the flow of time?
Many philosophers object for the reason that when events change in this sense, the change is not a real change in the event's essential, intrinsic properties, but only in its relationship to the observer. For example, saying the death of Queen Anne is an event that changes from present to past is much like saying her death changed because someone changed their attitude from approving of her death to disapproving of it. This extrinsic change in approval doesn't count as a real change in her death, and neither does the so-called change from present to past. So, it is concluded by these philosophers that the notion of time's flow is a myth. Attacking the notion of time's flow in this manner, Grünbaum said: "Events simply are or occur...but they do not 'advance' into a pre-existing frame called 'time.' ...time is a system of relations between events, and as events are, so are their relations. An event does not move and neither do any of its relations."
Instead of arguing that events change their properties, some advocates of the dynamic theory of time embrace the flow of time by saying that the flow is reflected in the change over time of truth values of a sentence such as "It is now raining." In response, critics suggest that the indexical sentence "It is now raining" is not used to express a single proposition that is true at some times and false at other times. It expresses a propositional function; that is, it is used to express different propositions on different occasions. The propositions that are expressed at each particular time, such as "It is raining at midnight on Jan. 1, 2000 in Chicago," do not change their truth values through time, but are timelessly true; and so the flow of time cannot be explained in terms of them. [For an explanation of the differences among sentences, statements, propositions, and utterances, see the article Truth. The word "now" is called an "indexical" because what it stands for depends on who says it, not just on its meaning. Other indexical words are "I" and "you" and "here."]
Recognizing this distinction between propositions and propositional functions, some advocates of the flow of time ask us to re-consider the situation by focusing on facts. "It is now raining" is a propositional function, they agree, and "It is raining at midnight on Jan. 1, 2000 in Chicago" is not. Assuming it did rain in Chicago then, this latter tenseless sentence can be used to express a proposition that is true when uttered on Jan. 1, 2000, but is not true in 1950. The tenseless fact did not exist in 1950, but it came into existence in 2000. This coming into existence of facts, the actualization of new states of affairs, is time's flow. What facts there are depends upon what time it is, and this is the key to the flow of time.
Even if time were to flow, there is the additional question of whether the flow can change. Can the flow on Friday be slower than the flow on Thursday? On a relational theory it is difficult to make sense of this, but on a substantival theory of time, the flow could slow down on Friday because fewer events happen then than on Thursday.
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8. What gives time its direction or "arrow"?
a. What needs to be explained
Time's arrow is evident in the process of mixing cool cream into hot coffee. You soon get lukewarm coffee, but you never notice the reverse--lukewarm coffee separating into a cool part and a hot part. Such is the way this irreversible thermodynamic process goes. Time's arrow is also evident when you upset the equilibrium of a birthday party by pricking a balloon. The air inside the balloon rushes out; it never stays in the balloon as it was before the pricking. So, the pricking starts an irreversible process. The arrow of a physical process is the way it normally goes, the way it normally unfolds through time. If a process normally goes one-way, we call it an "irreversible process." The amalgamation of the universe's irreversible processes produces the cosmic arrow of time, the master arrow. Usually this arrow is what is meant when one speaks simply of "time's arrow."
The goals of a theory of time's arrow are to understand why this arrow exists, what it would be like for the arrow to reverse direction, what exactly is the relationship between the direction of time and the direction of causation, and what the relationships are among the various more specific arrows of time--the various temporally asymmetric processes such as entropy increases [the thermodynamic arrow], causes preceding their effects [the causal arrow], our knowing the past more easily than the future [the psychological arrow], and so forth.
Actually, time is directional in two senses. In one sense, which is not the sense meant by the phrase "the arrow of time," time is directed from the future to the past. This is the sense in which any future event is temporally after any past event. Because this is implied by the very definition of the terms "future" and "past," to say "Time is directed from future to past" is to express a merely conventional truth of little interest to the philosophical community.
However, time is directed in a second sense, one that isn't merely a matter of the definition of the relevant terms but is about the particular ordering of events in time. It is what distinguishes events ordered by the happens-before relation from those ordered by its converse, the happens-after relation. It is still an open question in philosophy and science as to what it is about events that gives them this arrow.
Because physical processes do have an arrow you might think that an inspection of the basic physical laws would readily reveal time's arrow. It won't. With some apparently minor exceptions involving Higgs boson decay, all the basic laws of fundamental processes are time symmetric. This means that if a certain process is allowed by the equations, then that process reversed in time is also allowed, and either direction is as probable as the other. Maxwell's equations of electromagnetism, for example, can be used to predict that television can exist, but the equations don't tell us whether those signals arrive before or arrive after they are transmitted. In other words, these basic laws of science are insensitive to the arrow of time.
Let's suppose you could have a movie of a basic physical process such as two electrons bouncing off each other. You can't actually create this movie because the phenomenon is too small, but let's forget that fine point for a moment. If you had such a movie, you could run it forwards or backwards, and both showings would illustrate a possible process according to the basic laws of science, and they would be equally probable processes. That is, you couldn't tell from just looking at the movie whether you were looking at the original or at it being shown backwards in time. Time's arrow isn't revealed in this microscopic process.
The reason why this result is so interesting to scientists and philosophers is that, if you had a movie of the mixing of black coffee and white cream, then you could tell which way is the right way to show the movie. The arrow of time that was absent in the microscopic movie would be evident in the macroscopic movie. This difference between microscopic movies and macroscopic movies is odd because macroscopic processes are presumed to be composed of, and to be explainable in terms of, more basic processes. Why does the arrow of time appear in one movie but not the other? After all, either movie could be shown in either direction and still be showing a physically possible process; it's not impossible for brown coffee to un-mix into black coffee and white cream. The disappearance of time's arrow in the movie of the microscopic process, does not show that time itself fades away as you look at briefer and smaller processes; this is because there are still events happening, and so time does exist there. The principal question is why the arrow itself disappears.
b. Explanations or theories of the arrow
The first clue to answering this deep question was discovered in the mid-19th century by the German physicist Rudolf Clausius. He discovered an early version of the 2nd law of thermodynamics, which states that a closed system will evolve to be more disordered, its useful energy converting to heat. That is,
(a) 2nd Law: In a closed system, entropy increases.
Entropy is a measure of this disorder or of the conversion of useful to useless energy. Physicists immediately realized that they could explain time's arrow as entropy increase. The problem, though, was that the new kinetic theory of gases for which the concept of entropy was defined was supposed to provide the foundation for all gas behavior, yet this foundational theory is time symmetric. That is, the theory is insensitive to the arrow of time, to the distinction between past and future--because a moving molecule could just as well move in one direction as in the reverse direction. How were the physicists to resolve this apparent contradiction of having temporal asymmetry in processes that are supposed to be explained via a temporally symmetric theory?
Ludwig Boltzmann had an answer in 1872. It's also an answer to why the arrow of time emerges in the macroscopic movie but isn't evident in the microscopic movie. Boltzmann was the first to show how an irreversible macroscopic phenomenon may arise from reversible microscopic laws. He showed that irreversible macroscopic thermodynamic processes are irreversible because the probability of their actually reversing is insignificant. To be more specific, consider a container with hot gas in one half and cold gas in the other half. The gases mix and reach a common, lukewarm temperature. That is, they come to an equilibrium temperature. By applying the kinetic theory of gases to molecules obeying Newton's mechanics, Boltzmann discovered an important statistical asymmetry: there are more lukewarm microstates of the set of the gas' constituent molecules than there are microstates with separated hot and cold regions, so the system changes toward a common equilibrium temperature because it evolves in the "direction" of what is most probable. To express the point somewhat more precisely, let A be the set of microstates of an isolated container in which the left half of the container contains very hot gas and the right half of the container contains very cold gas, and there is no barrier separating the left half from the right. Let B be the microstates with lukewarm gas in both halves. Assume all the microstates are equally probable a priori. Boltzmann pointed out that the number of B states is dramatically larger than the number of A states, so the probability that one of the A states will soon evolve into one of the B states is almost one whereas the probability that a B state will soon evolve into an A state is almost zero. That is why the process of heat flow in an isolated gas is irreversible.
How does this explain the 2nd law of thermodynamics? Boltzmann redefined both the concept of entropy and the 2nd law. He redefined entropy as how probable a state is. Then he deduced a revised 2nd law:
(b) 2nd Law: In a closed system, entropy is likely to increase.
Although his actual proof was shown to depend on some probability theory and not merely on Newton's laws of motion, his treatment of entropy as being basically a statistical concept was broadly accepted, as was his claim that time's arrow is to be explained in terms of entropy increase.
Boltzmann's achievement soon had to confront two other obstacles, one from Henri Poincaré and one from Josef Loschmidt. A dynamic system is a system defined by the values of the positions and velocities of all the system's particles--such as the places and speeds of the atoms in a cup of coffee. Poincaré's recurrence theorem in statistical mechanics says every isolated dynamical system will eventually return to a state as close to the initial state as we might wish. Wait long enough, and the lukewarm coffee will separate into hot coffee and cool cream. This reversal would be expected to take billions of years, but that is still a finite time, so, strictly speaking, there are no irreversible processes. So, there is a contradiction between Poincaré's theorem and Boltzmann's proof. The second law implies that entropy probably increases, but Poincaré's theorem implies that, given a long period of time, entropy remains the same.
Nietzsche concluded that these Poincaré cycles rob human life of any ultimate moral progress. If a person demonstrates moral progress, the universe will eventually return to a state in which the person hasn't made this progress. Nietzsche concluded that the theorem implies that "God is dead."
To avoid the Poincaré problem, the second law needs another revision:
(c) 2nd Law: In a closed system, entropy is likely to increase for any period of time short compared to the Poincaré period for that system.
The problem raised by Poincaré is less of a problem for Boltzmann's treatment of time's arrow than is the Loschmidt Problem. Loschmidt pointed out that Boltzmann's statistical mechanics predicts for any point in time that not only should entropy be higher in the future but also it should be higher in the past. However, we know that it was not higher in the past. Here is a graph representing this knowledge.
The conclusion to be drawn from this is that entropy increase is only part of the story of time's arrow.
Loschmidt suggested that the low entropy in the past must be explained by what the initial conditions happened to be like at the beginning of the universe. Boltzmann agreed. Among cosmologists, this is now the generally accepted answer to the origin of time's arrow. Yet this answer leads naturally to the request for an explanation of the initial configuration of our universe. Is this temporally asymmetric initial boundary condition simply a brute fact? Are there no laws to explain the fact?
The Swiss physicist Walther Ritz and, more recently, Penrose and Prigogine, say we must not yet have found the true laws (or invented the best laws) underlying nature's behavior. We need to keep looking for basic, time asymmetrical laws in order to account for time's arrow.
Even if physicists agree someday on the initial conditions of the universe and on the laws of the universe, and thereby explain the entropy of the early universe and the cause of the cosmic arrow of time, there is no good reason to believe this theory would be a theory of everything. That theory wouldn't enable the prediction of your birth. The theory presumably would be a quantum mechanical theory. The probabilistic nature of quantum theory prevents the prediction of even the date that a radioactive uranium atom will fission into fragments, and it surely would prevent the prediction of your birth.
c. Multiple arrows
Consider the difference between time's arrow and time's arrows. For a process to be classified as an arrow of time, it must work differently or not at all if time were reversed. The direction of entropy change is the thermodynamic arrow. Here are some suggestions for additional arrows:
a. There are records of the past but not of the future.
b. It is easier to know the past than to know the future.
c. Light and radio waves spread out from, but never converge into, a point.
d. The universe expands rather than shrinks.
e. Causes precede their effects.
f. We see black holes but never white holes.
g. Conscious actions affect the future but not the past.
h. B meson decay, neutral kaon decay, and Higgs boson decay are each different in a time reversed world.
i. Quantum mechanical measurement collapses the wave function.
j. Possibilities decrease as time goes on.
Most physicists suspect all these arrows are linked so that we can't have some arrows reversing while others do not. The linkage may require as yet undiscovered laws. But could all the arrows reverse? That is, could the cosmic arrow of time have gone the other way? Most physicists suspect that the answer is "Yes, if the initial conditions of the universe at the Big Bang had been different."
d. Reversing time
Philosophers have gone on to ask interesting questions about different scenarios involving the reversal of time's arrow. Suppose the cosmic arrow of time were someday to reverse in a distant, populated region far away from Earth. Imagine what life would be like for the time reversed people. If they were just like us, then their past would be like our future. Would they become pre-cognitive and able to remember (what we call) the future? [Probably yes, but since their brain processes would be reversed, their experience wouldn't be different from ours.] If Aristotle is correct that the future, unlike the past, is undetermined or open, then their future would be open, too. But it's (like) our past. What do we conclude from this puzzle? Do we conclude that our past really is undetermined and open? That our past could change? And there are other questions. If the arrow of time reversed in some region, wouldn't people in that region grow younger? Surely someone can't become unborn. Or can they? Consider communication between the two regions. Could the message cross the border, or would it dissolve there? If a film were sent across the border to us, should we play it in the ordinary way or in reverse?
If the cosmic arrow of time were to reverse, it would be possible for our past to be re-created. This re-occurrence of the past is different than the re-living of past events via time travel. With time travel, the past is re-visited in the original order that the past events occurred; the past is not visited in reverse order.
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9. Is only the present real?
Have past objects, such as dinosaurs, slipped out of existence? Philosophers are divided on this question. More generally, there is no agreement about the reality of the past and future. The presentist viewpoint maintains that the past and the future are not real, and that only the present is real. Advocates of a growing past argue that, in addition, the past is real. Reality "grows" with the coming into being of determinate reality from an indeterminate or potential reality. "The world grows by accretion of facts," says Richard Jeffrey. Aristotle and C. D. Broad also advocate a growing past. Parmenides, Duns Scotus and A. N. Prior are presentists.
Opposing both presentism and the growing past theory, Hermann Weyl, J.J.C. Smart, and W.V.O. Quine argue that the objective world simply is. They say there is no objective ontological difference among the past, the present, and the future just as there is no ontological difference between here and there. This position is called eternalism or the block universe theory because it regards reality as a single block of spacetime with its time slices ordered by the temporally-before relation, as in a Minkowski spacetime diagram (although it is understood that not all spacetimes can be given Minkowski diagrams). It is mental perspectives only that divide the block into a past part, a present part, and a future part. William James coined the term "block universe," but the theory is also commonly called "eternalism" or the "static theory of time."
Although presentists say that there exist no dinosaurs, and eternalists say that dinosaurs are as real as anything in the present, a third camp of philosophers argue that the presentist-eternalist debate is merely verbal because each side is using the word "exists" in a different sense; the presentist uses it in a tensed sense, whereas the eternalist uses it in an untensed sense.
The presentist and the advocate of the growing past will usually unite in opposition to the block universe (eternalism) on the grounds that it misses the special "open" character of the future and the equally significant point that the present is so much more "vivid" to a conscious being than is any other time-slice of spacetime. The advocates of the block universe counter that only the block universe can make sense of relativity's implication that, if people are in certain relative motions, an event in person A's present can be in person B's future and in person C's past. Presentism and the growing-past theories must suppose that this event is both real and unreal because it's real for A but not real for B. Surely that conclusion is unacceptable, they claim. Their two key assumptions here are that relativity does provide an accurate account of the spatiotemporal relations among events, and that if there is some frame of reference in which two events are simultaneous, then if one of the events is real, so is the other.
Opponents of the block universe charge that it doesn't provide an accurate account of the way things are because it leaves out "the now" or "the present." This metaphysical dispute was fueled by Einstein who said:
Since there exists in the four dimensional structure no longer any slices which represent "now" objectively...it appears more natural to think of physical reality as a four dimensional existence instead of, as hitherto, the evolution of a three dimensional existence.
Many philosophers, however, do not agree with Einstein.
This philosophical dispute has taken a linguistic turn by focusing upon a question about language: "Are predictions true or false at the time they are uttered?" Those who believe in the block universe (and thus in the determinate reality of the future) will answer "Yes" while a "No" will be given by presentists and advocates of the growing past. The issue is whether contingent sentences uttered now about future events are true or false now rather than true or false only in the future at the time the predicted event is supposed to occur.
Suppose someone says, "Tomorrow the admiral will start a sea battle." And suppose that tomorrow the admiral orders a sneak attack on the enemy ships. And suppose that this action starts a sea battle. Advocates of the block universe argue that, if so, then the above sentence was true all along. Truth is eternal or fixed, they say, and "is true" is a tenseless predicate, not one that merely says "is true now." These philosophers point favorably to the ancient Greek philosopher Chrysippus who was convinced that a contingent sentence about the future is true or false, and it can't be any value in between such as "indeterminate". Many others, following a suggestion from Aristotle, argue that the sentence is not true until it's known to be true, namely at the time at which the sea battle occurs. The sentence wasn't true before the battle occurred. In other words, predictions have no (classical) truth values at the time they are uttered. Predictions fall into the "truth value gap." This position that contingent sentences have no truth values is called the Aristotelian position because many researchers throughout history have taken Aristotle to be holding the position in chapter 9 of On Interpretation--although today it is not so clear that Aristotle himself held it.
The principal motive for adopting the Aristotelian position arises from the belief that if sentences about future human actions are now true, then humans are fated (or determined) to perform those actions, and so humans have no free will. To defend free will, we must deny truth values to predictions.
The Aristotelian argument against predictions being true or false has been discussed as much as any in the history of philosophy, but it faces a series of challenges. First, if there really is no free will, or if free will is compatible with fatalism (or determinism), then the motivation to deny truth values to predictions is undermined.
Second, if it is true that you will perform an action in the future, it doesn't follow that now you won't perform it freely, nor that you aren't free to do otherwise, but only that you won't do otherwise. For more on this point about modal logic, see Foreknowledge and Free Will.
A third challenge arises from moral discussions about the interests of people who are as yet unborn. Quine argues that if we have an obligation to conserve the environment for these people, then we are treating them as being as real as the people around us now. Only the block universe view can make sense of this treatment.
A fourth challenge, from Quine and others, claims the Aristotelian position wreaks havoc with the logical system we use to reason and argue with predictions. For example, here is a deductively valid argument:
There will be a sea battle tomorrow.
If there will be a sea battle tomorrow, then we should wake up the admiral.
So, we should wake up the admiral.
Without the premises in this argument having truth values, that is, being true or false, we cannot properly assess the argument using the standard of deductive validity because this standard is about the relationships among truth values of the component statements. Unfortunately, the Aristotelian position says that some of these components are neither true nor false, so Aristotle's position is implausible.
In reaction to this fourth challenge, proponents of the Aristotelian argument claim that if Quine would embrace tensed propositions and expand his classical logic to a tense logic, he could avoid those difficulties in assessing the validity of arguments that involve sentences having future tense.
Russell, Quine, Grünbaum, and Horwich object to assigning special ontological status to the present. According to Quine, the analysts should in principle be able to eliminate the temporal indexical words because their removal is needed for fixed truth and falsity of our sentences [fixed in the sense of being eternal sentences whose truth values aren't relative because the indicator words have been replaced by times, places and names, and whose verbs are treated as tenseless], and having fixed truth values is crucial for the logical system used to clarify science. "To formulate logical laws in such a way as not to depend thus upon the assumption of fixed truth and falsity would be decidedly awkward and complicated, and wholly unrewarding," says Quine.
Philosophers are still very divided on the issues of whether only the present is real, what sort of logic is correct, and whether future contingent propositions have truth values.
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10. Are there essentially tensed facts?
What is the significance of saying that an event occurred in the past, the present, or the future? There are two major answers. One answer is that these distinctions represent objective features of reality that aren't captured by the popular "block universe" approach with its reliance on tenseless facts. This answer takes tenses very seriously and is called the tensed theory of time, or the A-theory in McTaggart's sense of A vs. B. A second answer to the question of the significance of references to tenses is that these distinctions are subjective features of the perspective from which we view the universe.
On the tenseless theory of time, or the B-theory, whether the birth of Mohammed occurs here depends on the speaker's perspective; similarly, whether the birth occurs now is equally subjective. The proponent of the tenseless view does not deny the importance or coherence of talk about the past but will say that talk about the past is really talk about our own relation to events. The assertion that Mohammed's birth is a past event might be analyzed as asserting that the birth event happens before the event of writing this sentence. Pointing out the relativity of simultaneity in Einstein's theory of relativity, the B-theorist also argues that an event's being present is relative to reference frame, a point that is missed by the A-theorist.
This controversy is often presented as a dispute about whether tensed facts exist, with advocates of the tenseless theory objecting to tensed facts. The primary function of tensed facts is to make tensed sentences true. For the purposes of making the point, let's uncritically accept the Correspondence Theory of Truth and apply it to the past tense sentence:
Custer died in Montana.
If we apply the Correspondence Theory directly to this sentence, we would say that
The sentence "Custer died in Montana" is true because it corresponds to the tensed fact that Custer died in Montana.
Opponents of tensed facts argue that the Correspondence Theory should be applied only indirectly. One approach, the classical tenseless approach, argues that the Correspondence Theory should be applied only to the result of analyzing away tensed sentences into equivalent sentences that don't use tenses. The sentence "Custer died in Montana" has this equivalent:
There is a time t such that Custer dies in Montana at time t, and time t is before the time of the utterance of the sentence "Custer died in Montana."
In this analysis, the verb dies is tenseless; it is not present tensed. Applying the Correspondence Theory to this new sentence yields:
The sentence "Custer died in Montana" is true because it corresponds to the tenseless fact that there is a time t such that Custer dies in Montana at time t, and time t is before the time of the utterance of "Custer died in Montana."
This analysis of tenses without appeal to tensed facts is challenged. It can work only for utterances, but a sentence can be true even if never uttered by anyone. There are other challenges. Roderick Chisholm and A. N. Prior claim that the "is" in the sentence "It's now midnight" is essentially present tensed because there is no translation using only tenseless verbs. Trying to analyze it as, say, "There is a time t such that t = midnight" is to miss the essential reference to the present in the original sentence. The latter sentence is always true, but the original is not, so the tenseless analysis fails. There is no escape by adding "and t is now" because this last indexical still needs analysis, and we've gone in a circle.
Chisholm and Prior say that true sentences using the temporal indexical terms "now," "before now," and "happened yesterday" are part of the facts of the world that science should account for, and science fails to do this because it doesn't recognize them as being real facts. Science so far restricts itself to eternal facts, such as in the Minkowski-like spacetime representation of events. These events are sets of spacetime points. For such events, the reference to time and place is explicit. A Minkowski spacetime diagram displays only what happens before what, but not which time is present time, or past, or future. What is missing from the diagram, say Chisholm and Prior, is some moving point on the time axis representing the observer's "now" as time flows up the diagram.
In the same spirit, Michael Dummett argues that you can have a complete description of a set of objects even if you haven't said which objects are near and which are far, but you cannot have a complete description of those objects without specifying which events are happening now and which are not.
Earlier, Prior [1959] had argued that after a painful event,
one says, e.g., "Thank goodness that's over," and [this]...says something which it is impossible that any use of a tenseless copula with a date should convey. It certainly doesn't mean the same as, e.g., "Thank goodness the date of the conclusion of that thing is Friday, June 15, 1954," even if it be said then. (Nor, for that matter, does it mean "Thank goodness the conclusion of that thing is contemporaneous with this utterance." Why should anyone thank goodness for that?).
D. H. Mellor, who advocates a newer subjective theory of tenses, argues that the truth conditions of any tensed sentence can be explained without tensed facts even if Chisholm and Prior are correct that some tensed sentences can't be translated into tenseless ones. Mellor would say it is not the pastness of the painful event that explains why I say, "Thank goodness that's over." My gladness is explained by my belief that the event is past, plus its being true that the event occurs before now. Tenseless facts can explain all this. In addition, tenseless sentences can be used to explain the logical relations between tensed sentences: that one tensed sentence implies another, is inconsistent with yet another, and so forth. Then Ockham's Razor is applied. If we can do without essentially tensed facts, then we should say essentially tensed facts do not exist. To summarize, tensed facts were presumed to be needed to account for the truth of tensed talk; but the analysis shows that ordinary tenseless facts are adequate. So, there are no essentially tensed facts.
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11. What is temporal logic, the symbolic logic of time?
Temporal logic is the representation of information about time by using the methods of symbolic logic. The classical approach to temporal logic is via tense logic, a formalism that adds tense operators to an existing system of symbolic logic. The pioneer in the late 1950's was A. N. Prior. He created a new symbolic logic to describe our use of time words such as "now," "happens before," "afterwards," "always," and "sometimes". The relationships that propositions have to the past, present, and future help to determine their truth-value. A proposition, such as "Socrates is sitting down" is allowed to be true at one time and false at another time.
Prior was the first to appreciate that time concepts are similar in structure to modal concepts such as "it is possible that" and "it is necessary that," and so he adapted modal propositional logic for his tense logic. Dummett and Lemmon also made major, early contributions to tense logic.
In one standard system of the logic of past time, the S4.3 system, the usual modal operator "it is possible that" is re-interpreted to mean "at some past time it was the case that." Let the letter "P" represent this operator, and add to the axioms of classical propositional logic the modal-like axiom P(p v q) iff Pp v Pq. The axiom says that for any two present-tensed propositions p and q, at some past time it was the case that p or q if and only if either at some past time it was the case that p or at some past time it was the case that q. The S4.3 system's key axiom is the equivalence
Pp & Pq iff P(p & q) v P(p & Pq) v P(q & Pp).
This axiom captures our ordinary conception of time as a linear succession of states of the world. Another axiom might state that if Q is true, then it will always be true that Q has been true at some time. Prior and others have suggested a wide variety of axioms for tense logic, but logicians still disagree about what axioms are needed to capture correct beliefs about time as theorems. Some extension of classical tense logic is needed to express "Q has been true for the past three days."
The concept of being in the past is usually treated by metaphysicians as a predicate that assigns properties to events, but in this tense logic the concept is treated as an operator P upon propositions, and this difference in treatment is objectionable to some metaphysicians.
The other major approach to temporal logic does not use a tense logic. Instead, it formalizes temporal reasoning within a first-order logic without modal-like tense operators. This so-called method of "temporal arguments" adds an additional variable, a time argument, to any predicate involving time in order to indicate how its satisfaction depends on time. A predicate such as "is less than seven" doesn't involve time, but the predicate "is resting" does. If "x is resting" is represented classically as R(x), where R is a one-argument predicate, then it would be represented in temporal logic as R(x,t) and would be interpreted as saying x has property R at time t. R has been changed to a two-argument predicate by adding a "temporal argument." The time variable "t" is treated as a new sort of variable with its own axioms. These axioms might allow time to be a dense linear ordering without endpoints, or to be even more like the real numbers.
Occasionally the method of temporal arguments uses a special constant symbol, say "n", to denote now, the present time. This helps with the translation of common temporal statements. For example, the statement that Q has always been true may be translated into first-order temporal logic as
(t)[(t < n) â Q(t)].
The first person to give a clear presentation of the implications of treating declarative sentences as being neither true nor false was the Polish logician Jan Lukasiewicz in 1920. To carry out Aristotle's suggestion that future contingent sentences don't yet have truth values, he developed a three-valued symbolic logic, with all grammatical declarative sentences having the truth-values of True, False, or else Indeterminate [T, F, or I]. Contingent sentences about the future, such as Aristotle's prediction that there will be a sea battle tomorrow, are assigned an I. Truth tables for the connectives of propositional logic are redefined to maintain logical consistency and to maximally preserve our intuitions about truth and falsehood. See Haack (1974) for more details about this application of three-valued logic.
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13. References and Further Reading
Callender, Craig, and Ralph Edney. Introducing Time, Totem Books, USA, 2001.
A cartoon-style book covering most of the topics in this article in a more elementary way. Each page is two-thirds graphics and one-third text.
Davies, Paul. About Time: Einstein's Unfinished Revolution, Simon & Schuster, 1995.
An easy to read survey of the impact of the theory of relativity on our understanding of time.
Davies, Paul. How to Build a Time Machine, Viking Penguin, 2002.
A popular exposition of the details behind the possibilities of time travel.
Deutsch, David and Michael Lockwood, "The Quantum Physics of Time Travel," Scientific American, pp. 68-74. March 1994.
An investigation of the puzzle of getting information for free by traveling in time.
Grünbaum, Adolf. "Relativity and the Atomicity of Becoming," Review of Metaphysics, 1950-51, pp. 143-186.
An attack on the notion of time's flow, and a defense of the treatment of time and space as being continua and of physical processes as being aggregates of point-events.
Haack, Susan. Deviant Logic, Cambridge University Press, 1974.
Chapter 4 contains a clear account of Aristotle's argument for truth-value gaps, and its development in Lukasiewicz's three-valued logic.
Hawking, Stephen. "The Chronology Protection Hypothesis," Physical Review. D 46, p. 603, 1992.
Reasons for the impossibility of time travel.
Hawking, Stephen. A Brief History of Time, Updated and Expanded Tenth Anniversary Edition, Bantam Books, 1996.
A leading theoretical physicist provides introductory chapters on space and time, black holes, the origin and fate of the universe, the arrow of time, and time travel.
Horwich, Paul. Asymmetries in Time, The MIT Press, 1987.
A monograph that relates the central problems of time to other problems in metaphysics, philosophy of science, philosophy of language and philosophy of action.
Katzenstein, Larry, ed. A Matter of Time, Scientific American Special Edition: A Matter of Time, vol. 16, No. 1, 2006.
A collection of Scientific American articles about time.
Krauss, Lawrence M. and Glenn D. Starkman, "The Fate of Life in the Universe," Scientific American Special Edition: The Once and Future Cosmos, Dec. 2002, pp. 50-57.
Discusses how intelligent life might adapt to and survive the expansion of the universe.
Lasky, Ronald C. "Time and the Twin Paradox," in Katzenstein, pp. 21-23.
A short, but careful and authoritative analysis of the twin paradox, with a graph showing how each twin would view his and the other's clocks during the trip.
Le Poidevin, Robin and Murray MacBeath, The Philosophy of Time, Oxford University Press, 1993.
A collection of twelve influential articles on the passage of time, subjective facts, the reality of the future, the unreality of time, time without change, causal theories of time, time travel, causation, empty time, topology, possible worlds, tense and modality, direction and possibility, and thought experiments about time. Difficult reading for undergraduates.
Mellor, D. H. Real Time II, International Library of Philosophy, 1998.
This monograph presents a subjective theory of tenses. Mellor argues that the truth conditions of any tensed sentence can be explained without tensed facts.
Prior, A. N. "Thank Goodness that's Over," Philosophy, 34 (1959), p. 17.
Argues that a tenseless or B-theory of time fails to account for our relief that painful past events are in the past rather than in the present.
Prior, A. N. Past, Present and Future, Oxford University Press, 1967.
A pioneering work in temporal logic, the symbolic logic of time, which permits propositions to be true at one time and false at another.
Prior, A. N. "The Notion of the Present," Studium Generale, volume 23, 1970, pp. 245-8.
A brief defense of presentism, the view that the past and the future aren't real.
Rennie, John. (ed.). Scientific American Special Edition: A Matter of Time, volume 16, no. 1, 2006.
A series of popular science articles on many of the topics in this article.
Salmon, Wesley C. (ed.). Zeno's Paradoxes, The Bobbs-Merrill Company, Inc., 1970.
A collection of the most influential articles about Zeno's Paradoxes that were written in the period from 1911 to 1965. Salmon provides an excellent annotated bibliography of further readings.
Sciama, Dennis. "Time 'Paradoxes' in Relativity," in The Nature of Time edited by Raymond Flood and Michael Lockwood, Basil Blackwell, 1986, pp. 6-21.
A good account of the twins paradox.
Shoemaker, Sydney. "Time without Change," Journal of Philosophy, 66 (1969), pp. 363-381.
A thought experiment designed to show us how time could exist even without any change in the universe.
Sorabji, Richard. Matter, Space, & Motion: Theories in Antiquity and Their Sequel. Cornell University Press, 1988.
Chapter 10 discusses ancient and contemporary accounts of circular time.
Tegmark, Max. "Parallel Universes," Scientific American, May 2003, pp. 40-51.
A clear presentation of the multiverse theory of kinds of parallel universes. Attention is directed toward some of the philosophical implications. He argues that you must have an exact duplicate of yourself, down to the very atoms and memories, in another galaxy that is about 10 to the 10 to the 28 meters from Earth.
Van Fraassen, Bas C. An Introduction to the Philosophy of Time and Space, Columbia University Press, 1985.
An advanced undergraduate textbook by an important philosopher of science.
Veneziano, Gabriele. "The Myth of the Beginning of Time," Scientific American, May 2004, pp. 54-65.
An account of string theory's impact on our understand of time's origin. Veneziano hypothesizes that our Big Bang was not the origin of time but simply the outcome of a preexisting state. Reprinted in Katzenstein.
Whitrow. G. J. The Natural Philosophy of Time, Second Edition, Clarendon Press, 1980.
A broad survey of the topic of time and its role in physics, biology, and psychology. Pitched at a higher level than the Davies books.
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Author Information:
Bradley Dowden
Email: dowden@csus.edu
California State University, Sacramento
© 2006